428 research outputs found
Locality of not-so-weak coloring
Many graph problems are locally checkable: a solution is globally feasible if
it looks valid in all constant-radius neighborhoods. This idea is formalized in
the concept of locally checkable labelings (LCLs), introduced by Naor and
Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree
graphs, every LCL problem belongs to one of the following classes:
- "Easy": solvable in rounds with both deterministic and
randomized distributed algorithms.
- "Hard": requires at least rounds with deterministic and
rounds with randomized distributed algorithms.
Hence for any parameterized LCL problem, when we move from local problems
towards global problems, there is some point at which complexity suddenly jumps
from easy to hard. For example, for vertex coloring in -regular graphs it is
now known that this jump is at precisely colors: coloring with colors
is easy, while coloring with colors is hard.
However, it is currently poorly understood where this jump takes place when
one looks at defective colorings. To study this question, we define -partial
-coloring as follows: nodes are labeled with numbers between and ,
and every node is incident to at least properly colored edges.
It is known that -partial -coloring (a.k.a. weak -coloring) is easy
for any . As our main result, we show that -partial -coloring
becomes hard as soon as , no matter how large a we have.
We also show that this is fundamentally different from -partial
-coloring: no matter which we choose, the problem is always hard
for but it becomes easy when . The same was known previously
for partial -coloring with , but the case of was open
Slow roll in simple non-canonical inflation
We consider inflation using a class of non-canonical Lagrangians for which
the modification to the kinetic term depends on the field, but not its
derivatives. We generalize the standard Hubble slow roll expansion to the
non-canonical case and derive expressions for observables in terms of the
generalized slow roll parameters. We apply the general results to the
illustrative case of ``Slinky'' inflation, which has a simple, exactly
solvable, non-canonical representation. However, when transformed into a
canonical basis, Slinky inflation consists of a field oscillating on a
multi-valued potential. We calculate the power spectrum of curvature
perturbations for Slinky inflation directly in the non-canonical basis, and
show that the spectrum is approximately a power law on large scales, with a
``blue'' power spectrum. On small scales, the power spectrum exhibits strong
oscillatory behavior. This is an example of a model in which the widely used
solution of Garriga and Mukhanov gives the wrong answer for the power spectrum.Comment: 9 pages, LaTeX, four figures. (V2: minor changes to text. Version
submitted to JCAP.
Dark Before Light: Testing the Cosmic Expansion History through the Cosmic Microwave Background
The cosmic expansion history proceeds in broad terms from a radiation
dominated epoch to matter domination to an accelerated, dark energy dominated
epoch. We investigate whether intermittent periods of acceleration are possible
in the early universe -- between Big Bang nucleosynthesis (BBN) and
recombination and beyond. We establish that the standard picture is remarkably
robust: observations of anisotropies in the cosmic microwave background exclude
any extra period of accelerated expansion between 1 \leq z \lesssim 10^5
(corresponding to 5\times10^{-4}\ {\rm eV} \leq T \lesssim 25\ {\rm eV}).Comment: 7 pages, 5 figure
Constraining Models of New Physics in Light of Recent Experimental Results on
We study extensions of the Standard Model where the charged current weak
interactions are governed by the CKM matrix and where all tree-level decays are
dominated by their Standard Model contribution. We constrain both analytically
and numerically the ratio and the phase difference between the New Physics and
the Standard Model contributions to the mixing amplitude of the neutral
system using the experimental results on , ,
and . We present new results concerning models with minimal
flavor violation and update the relevant parameter space. We also study the
left-right symmetric model with spontaneously broken CP, probing the viability
of this model in view of the recent results for and other
observables.Comment: 32 pages, including 9 figures, typos and error in fig. 1 corrected,
minor modificiation in the text, conclusions unchanged, to appear in PR
How Long It Takes for an Ordinary Node with an Ordinary ID to Output?
In the context of distributed synchronous computing, processors perform in
rounds, and the time-complexity of a distributed algorithm is classically
defined as the number of rounds before all computing nodes have output. Hence,
this complexity measure captures the running time of the slowest node(s). In
this paper, we are interested in the running time of the ordinary nodes, to be
compared with the running time of the slowest nodes. The node-averaged
time-complexity of a distributed algorithm on a given instance is defined as
the average, taken over every node of the instance, of the number of rounds
before that node output. We compare the node-averaged time-complexity with the
classical one in the standard LOCAL model for distributed network computing. We
show that there can be an exponential gap between the node-averaged
time-complexity and the classical time-complexity, as witnessed by, e.g.,
leader election. Our first main result is a positive one, stating that, in
fact, the two time-complexities behave the same for a large class of problems
on very sparse graphs. In particular, we show that, for LCL problems on cycles,
the node-averaged time complexity is of the same order of magnitude as the
slowest node time-complexity.
In addition, in the LOCAL model, the time-complexity is computed as a worst
case over all possible identity assignments to the nodes of the network. In
this paper, we also investigate the ID-averaged time-complexity, when the
number of rounds is averaged over all possible identity assignments. Our second
main result is that the ID-averaged time-complexity is essentially the same as
the expected time-complexity of randomized algorithms (where the expectation is
taken over all possible random bits used by the nodes, and the number of rounds
is measured for the worst-case identity assignment).
Finally, we study the node-averaged ID-averaged time-complexity.Comment: (Submitted) Journal versio
Are the New Physics Contributions from the Left-Right Symmetric Model Important for the Indirect CP Violation in the Neutral B Mesons?
Several works analyzing the new physics contributions from the Left-Right
Symmetric Model to the CP violation phenomena in the neutral B mesons can be
found in the literature. These works exhibit interesting and experimentally
sensible deviations from the Standard Model predictions but at the expense of
considering a low right scale \upsilon_R around 1 TeV. However, when we stick
to the more conservative estimates for \upsilon_R which say that it must be at
least 10^7 GeV, no experimentally sensible deviations from the Standard Model
appear for indirect CP violation. This estimate for \upsilon_R arises when the
generation of neutrino masses is considered. In spite of the fact that this
scenario is much less interesting and says nothing new about both the CP
violation phenomenon and the structure of the Left-Right Symmetric Model, this
possibility must be taken into account for the sake of completeness and when
considering the see-saw mechanism that provides masses to the neutrino sector.Comment: LaTex file. 19 pages, 4 figures. Change in the way the paper address
the problem. As a result, change in title, abstract, and some sections.
Conclusions unchanged. Version to appear in Foundations of Physics Letter
Signature of short distance physics on inflation power spectrum and CMB anisotropy
The inflaton field responsible for inflation may not be a canonical
fundamental scalar. It is possible that the inflaton is a composite of fermions
or it may have a decay width. In these cases the standard procedure for
calculating the power spectrum is not applicable and a new formalism needs to
be developed to determine the effect of short range interactions of the
inflaton on the power spectrum and the CMB anisotropy. We develop a general
formalism for computing the power spectrum of curvature perturbations for such
non-canonical cases by using the flat space K\"all\'en-Lehmann spectral
function in curved quasi-de Sitter space assuming implicitly that the
Bunch-Davis boundary conditions enforces the inflaton mode functions to be
plane wave in the short wavelength limit and a complete set of mode functions
exists in quasi-de Sitter space. It is observed that the inflaton with a decay
width suppresses the power at large scale while a composite inflaton's power
spectrum oscillates at large scales. These observations may be vindicated in
the WMAP data and confirmed by future observations with PLANCK.Comment: 17 pages, 4 figures, Extended journal version, Accepted for
publication in JCA
CP asymmetries in B0 decays in the left-right model
We study time dependent CP asymmetries in B^0_{d,s} decays in the left-right
model with spontaneous breakdown of CP. Due to the new contributions to
B^0-\bar B^0 mixing the CP asymmetries can be substantially modified. Moreover,
there can be significant new contributions to the -meson decay amplitudes
from the magnetic penguins. Most promising for detection of the new physics in
the planned factories is that the CP asymmetries in the decays B--> J/\psi
K_S and B--> \phi K_S which are supposed to be equal in the standard model can
differ significantly in this class of models independently of the results in
the measurements of B--> X_s \gamma.Comment: Revised version, to appear in PR
Constraining New Physics with the CDF Measurement of CP Violation in
Recently, the CDF collaboration has reported a measurement of the CP
asymmetry in the decay: . We
analyze the constraints that follow from this measurement on the size and the
phase of contributions from new physics to B-\barB mixing. Defining the
relative phase between the full amplitude and the Standard Model
contribution to be , we find a new bound: \sin2\theta_d\gsim-0.6
(-0.87) at one sigma (95% CL). Further implications for the CP asymmetry in
semileptonic B decays are discussed.Comment: 13 pages, harvmac, 3 figures; v2: a discussion of new physics effects
on tree level decays added; references added; accepted for publication in
Physical Review Letter
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